Any Brexit deal negotiated with the EU must not “trap” the UK in an open-ended customs arrangement, Commons leader Andrea Leadsom has told the BBC.

The Brexiteer urged Tories to back the PM and said she was “sticking in government” to work for a good deal.

But the UK must be able to exit any temporary customs arrangement aimed at avoiding a hard Irish border, she said.

On Friday, pro-Remain minister Jo Johnson quit the government and called for a new referendum on the final deal.

Mrs Leadsom, who Theresa May beat to the Conservative leadership in 2016, told BBC 5 live there would “not be a second referendum” if MPs rejected the final withdrawal deal. But she said she believed “most members of Parliament would vote for a deal rather than no deal”.

Asked if other ministers might resign, she said she was not expecting any, adding: “I do urge colleagues to support the prime minister.

“We are at a very difficult stage. What we have to do is hold our nerve and keep negotiating, make sure that we are pointing out to our EU friends and neighbours that it’s in all of our interests to get a good deal and just get it over the line.”

Negotiating a “backstop” – a legally-binding mechanism for keeping an open border between Northern Ireland and the Republic of Ireland until the UK and EU agree their future relationship – remains the main obstacle in the way of a wider agreement between the two sides.

If sufficient progress is made on the issue in the next few days, it is thought a special cabinet meeting could be held next week for ministers to approve the draft agreement on the terms of the UK’s exit.

One option could be for the whole of the UK to remain temporarily aligned to the EU’s customs union, avoiding the need for customs checks at the border until a free trade deal is ready.

But Leave campaigners want a clear exit strategy from any such arrangement – something which is unacceptable to the EU, which says any “backstop” must apply “unless and until” it is no longer needed.

Mrs Leadsom said while the backstop was not a “likely scenario”, she said it must involve a customs arrangement “that would include the entire UK” that “must be time limited”.

She added: “The UK cannot be forced to remain in a customs arrangement. Now how that specifically works is exactly what is being discussed and negotiated on now. The UK cannot be held against its will in a customs arrangement.

“It cannot be a decision that can be overturned by the EU. It must be capable for the UK to decide to leave that customs arrangement, and it cannot be something that the EU can then hold us to.

“Frankly it’s because that would be to then fail to fulfil on the will of the people expressed at the referendum, and I very much doubt that we would get it through Parliament.”

Asked what she would do if the final withdrawal deal did not meet her criteria, the Commons leader said she did not want to “play games with what I might or might not do” as she was working hard to get a deal that honoured the 2016 referendum result.

On Thursday, Brexit-backing cabinet minister Liam Fox also told reporters that the UK must have the power to end any post-Brexit “backstop”.

Brexit is due to happen on 29 March 2019, as a result of the referendum in June 2016 in which people voted by 51.9% to 48.1% for the UK to leave the European Union.

If a Brexit deal is agreed between the UK and the EU, it then has to be approved by the House of Commons and the remaining EU member states.